Alan Pak Tao Lau Supervisor: Prof. F.R. Kschischang Date: April 2 nd , 2004

Optimal Feedback Quantization Schemes for Multiuser Diversity Systems_________________________________ Alan Pak Tao Lau Supervisor: Prof. F.R. Kschischang Date: April 2nd, 2004

Wireless Fading Channels • Fluctuations of channel quality over time • Constructive and destructive interference due to multi-paths

Downlink Multiuser Fading Channel • Operates on a time-division basis (e.g. GSM, HDR) • Transmission sometimes scheduled to users in deep fade

Multiuser Diversity • Each user measures and feeds back instantaneous channel quality for scheduling • Long term throughput maximized by always serving the user with the best channel quality

Feedback Quantization • Each user digitizes and feeds back their current channel quality through their feedback channel • What should they feedback?

Feedback Quantization • Each user digitizes and feeds back their current channel quality through their feedback channel • What should they feedback? • Information rate, channel coefficient, SNR etc.

Feedback Quantization • Each user digitizes and feeds back their current channel quality through their feedback channel • What should they feedback? • Information rate, channel coefficient, SNR etc. • Any quantity can be fed back if is any monotonically increasing function

Channel Quality Index • where is the c.d.f. of • is uniformly distributed in [0,1] • Denote as the channel quality index for user i • Multiuser diversity

Probability of Error • Number of users K=2 • Number of quantization levels per user L=2 • Assumptions: independent fading, perfect estimation of s for users, perfect feedback channel

Probability of Error • Number of users K=2 • Number of quantization levels per user L=2 • Assumptions: independent fading, perfect estimation of s for users, perfect feedback channel • Probability of error

Problem Statement • Given independent and uniformly distributed in [0,1] and L quantization levels for each index, design quantization rules Qk,together with a decision rule D that will optimize a certain performance criterion • Criterion: minimize • The set of boundaries for all K users uniform quantization scheme

for 2 users, 2 levels Decision rule D Maximum A Postereri (MAP) rule Minimum when

for 2 users, L levels • while • Optimal scheme saves 1 bit as L goes large

Interleaving Property • Theorem 1: In a system of K users and L levels with quantization boundaries , the set user i for minimum

for K users, L levels

Performance for K=5 • Optimal scheme saves more than 1 bit

Approximation Scheme

Approximation Scheme • For K users, L levels, approximation scheme

Numerical Results • At K=30,L=16, optimal scheme requires L=3 while approximation scheme requires L=10

Quantizing for Maximum Throughput_________________________________________________ • Minimize = minimize • Maximize throughput = minimize

Optimal Weighting Function • Maximize expected throughput = minimize

for K users and L levels • For a system with i.i.d Rayleigh fading

Numerical Results • At K=30,L=16, optimal scheme requires L=3 while approximation scheme requires L=8

Location of Boundaries • Generally skewed towards 1 • Boundaries for more skewed towards 1

Implementation Issues • Base station updates K, user identity known for each user • Adding bias for approximation scheme • Only quantization for minimal is possible if distributions not identical, but it ensures proportional fairness

Summary • Distributed scalar quantization schemes to minimize and maximize throughput • Designed jointly, implemented separately • Substantial improvements over uniform quantization scheme

Summary (cont’d) • Low complexity approximation scheme shown to outperform the uniform quantization scheme • Implementation issues of optimal quantization schemes

Alan Pak Tao Lau Supervisor: Prof. F.R. Kschischang Date: April 2 nd , 2004